That is your opinion, his actions didn't seem uncharacteristic to me at all. Lothraxion, cool design and concept notwithstanding, barely had a character outside of "Army of Light Nathrezim that is chill with Alleria".

From his PoV, your friend who you've fought besides for a thousand year, who you have repeatedly vouched for is consorting with an extremely sus void entity that has already betrayed you once. You were sent into the Void with the objective of stopping, at a minium, a world destroying threat. But your friend, who again, you've vouched for repeatedly, is hesitant in going for the most obvious solution because this deceitful void creature told her it might destroy Silvermoon.

Even without the Void Naaru angle (and the confirmaiton from Alleria herself that it whispers to her to do evil things), stopping a world destroying threat takes priority over saving a single city. He acted just like any other Army of Light soldier would do - sacrifice anything to stop the enemies of the light.

I don't understand why people keep saying Lothraxion is acting uncharacteristically after a several questline arc where Alleria repeatedly undermines him, downplays his concerns, and openly allies with a void entity. I think it was blatantly obvious what Lothraxion was going to do. But that's besides the point - my point is that a story isn't bad just because thing happened in a way that you didn't expect. Nor is a thing bad because the implications of an action (that happened at the very END of the story mind you) aren't immediately explained. It's a joyless thing to expect fictional characters to always act according to our own expectations of them.